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Unformatted text preview: Quiz 1 Problem 1 (10) Describe a procedure for determining if the intersection of two ﬁnite sets ,say
{a1,a2,...,an} and {171,152, Wing}, is a subset of another ﬁnite sets, say {c1,...,cm}. Express the
procedure in a pseudocode. Count the number of steps it takes for the program to halt. W94“ sew? (hi“M 7 i é»~~,i3, mes) A' i 422 W3 f2: 1:) "5) 27, 7’, "z “3
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m V” J Antr :6 51“ AM 5? c, gr; an Vol...) Quiz 3 Problem 1 (5) Prove that if f is 0(9) and g is 0(h) then f is 0(h). (Write this in English
sentences. Explain the meaning of each symbol that you will be using, and for each symbol explain 
how or why one can get the object denoted by the symbol). (e063? Agfofé? “*7?€0CA§ ‘
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{M tea/ﬁ— .< (7% 90% 4' 445$) 74%; A/ WEI: LS‘; l‘Q—nv, Q’r J/i Problem 2 (5) Prove that iff : S —+ Y and if X, Z are subsets of S, then f(X U Z) : f(X) U
f {Write this in Engh'sh sentences. Explain the meaning of each symbol that you will be using,
and for each symbol explain how or why one can get the object denoted by the symbol). a? .
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"x 4 W") Mg Y"? array fl“ or FM {LA {S ’7‘ 4M {SaraAl}, 5? Alia] 1'? r is M WI’H‘x £511) is m ffy)‘ Inc X131“ aﬁga) is _/A F(—Z—). . t o/
ﬂnggc’lgL 5%,ch a? an; "L inc “Fa/{7‘ (Liam, 47? 5/ X) 4V0 is A chub—Fm) M m ¥(?U75). "L? X {’5 A web 3( or 27, 100K 4” X/ 940 z; 2% 01514:! ’{ “F179, arm MM é,” “PL Mei. (mum mm A 465”! 2;, regime can ﬂy wen/1% 4H M 1"? [S [*3 1C AU?) ﬁnd a" ﬁlm )CCAU}):.FCX)U—PIZU ‘ J?§\ ig‘mw No [736% Quiz 4 COMMENT: This quiz is out 0f 20 points. Your grade for this quiz will be divided by 2, to,
make sure that all quizzes or out of 10. Problem 1 (5) Using Euclidian Algorithm ﬁnd the greatest common divisor of 385 and 924. 3‘55 cavew u :3v52 % , ‘7’” ’5“ ya! (moo =77 .
15H 4?; 3?: ‘7 z + 7‘7
23%”; 1222 Problem 2 (15) Shoe that if}? is a. prime number then either 4mg 5 1(modp) has no solutions or
the only solutions of it are integers 1: such that a: E 1J—jg—1(n10d;o) or x E P—Elﬁnodp). [Hint This is
like the homework problem. First try to ﬁgure out for which p’s there are no solutions. Then show
that for other p’s all solutions have to be of the given form. The last step is to show that every x
of the given form is a solution. You can use the back of this paper] . ,, 40:12; \ c
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1 OJ )4 [1 at." 1 +17 2 f; Gtzj’gﬂ'ﬂ/u‘hnf. 7%. ‘ Flt,ng ’97"? “is/2"] ammﬁh/ Z \
/ nﬁsém Quiz 5 Problem 1 (5) Using Fermat’s Little T hearem, Show that 368 E 13(m0d17). Pr} 474,39 t7
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’€ 7 l3 “3“”? I? Problem 2 { 5 ) Prove that there are inﬁnitely many primes of the form 616 + 5, and explain why '
doesn’t the same proof imply that there are inﬁnitely many primes of the form 616 + 1. atpﬂagy {[7 7 f), {an [A d t &I/ [army/5
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This note was uploaded on 04/19/2008 for the course MATH 55 taught by Professor Strain during the Fall '08 term at University of California, Berkeley.
 Fall '08
 STRAIN
 Math

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